9
votes
Accepted
What exactly is the unique union of a family of sets?
The uniqueness is in the formula used to define the "unique union":
$\{x \mid ∃!A(A∈F \land x∈A) \}$.
This means that if an element $a$ belongs to e.g. two sets $A_1$ and $A_2$ of the ...
- 93.2k
3
votes
Accepted
Un-definability of graphs with bounded out-degree
here is the compactness argument @Noah alludes to. Suppose for contradiction that bounded out degree is definable by some P. Then consider the following for each n:
$d_n: \exists x_1,...,x_n [\...
- 491
1
vote
Example of a sentence of the language $\{+,0,S\}$, unprovable in Q1--Q5 but provable in Q?
I can't solve the original problem yet.
The best I can do is come up with a statement that's a theorem of the reduced theory of Robinson arithmetic plus a fictitious Q8 (shown below) but not of Q1-Q5.
...
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